Mathematics

# If $\displaystyle \frac{x}{(x-3)(x-2)}= \frac{3}{x-3}+\frac{A}{x-2}$, then $A$=

$-2$

##### SOLUTION
Given, $\displaystyle \frac{x}{(x-3)(x-2)}= \frac{3}{x-3}+\frac{A}{x-2}$         ....(1)
Resolving into partial fraction,
$\displaystyle \frac { x }{ (x-3)(x-2) } =\frac { A }{ x-2 } +\frac { B }{ x-3 }$      .....(2)
$x=A(x-3)+B(x-2)$
When $x=3, B=3$
When $x=2, A=-2$
Put these values in (2),
$\displaystyle \frac { x }{ (x-3)(x-2) } =\frac { -2 }{ x-2 } +\frac { 3 }{ x-3 }$
Hence, $A=-2$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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